JPS6214776B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION By irradiating a metal or other polycrystalline sample with X-rays and measuring the diffraction angle, the residual stress of the sample can be determined. Conventionally, this stress measurement method involves changing the incident angle of the X-rays within a plane perpendicular to the sample surface, including the X-rays incident on the sample surface, and measuring the X-rays diffracted into the plane at each incident angle. By determining the diffraction angle, the stress in the plane direction on the sample surface was determined. Therefore, in order to determine the direction and magnitude of the principal stress using this method, it is necessary to measure stress in at least three directions, making the measurement extremely complicated. Furthermore, since the incident angle of the X-rays on the sample surface must be set to, for example, 90 degrees and 45 degrees, and the difference in diffraction angles between these angles is determined, a large space is required around the measurement point, and it is necessary to It was difficult to measure the stress at The present invention provides a stress measurement method that does not have the drawbacks mentioned above.

FIG. 1 is a diagram for explaining the principle of the present invention.
A thin parallel X-ray χ with a single wavelength is made incident on the measurement point 0 on the polycrystalline sample surface as shown by the arrow. Let z be the normal to the sample surface set at this point 0, and let x and y be the orthogonal coordinate axes set on the sample surface. Since the incident X-ray χ is diffracted from point 0 along the generating line of the conical surface with the X-ray as the axis, the group of straight lines perpendicular to the lattice plane of the crystal that contributes to the generation of the diffracted X-ray also becomes a point. It forms a substantially conical surface with 0 as the apex. Let S be the diffraction surface normal ring where this conical surface includes an arbitrary point 0' on the straight line containing the incident X-ray χ and intersect with a plane perpendicular to the straight line 00', and let S be the curve where the diffracted X-ray intersects with the above plane. It is represented by T.

Let P' be the point where the diffraction surface normal ring S intersects the plane containing the normal z and the direction 00' of the incident X-ray, and let Q' be the foot of the normal line drawn from point P' to the xy plane. Also, let Q be the foot of the normal line drawn from any point P on the normal ring S to the xy plane, and let the normal z and the straight line 00' be 0.
Let the angles between P be ψ0 and ψ, respectively. Further, let the angles between the axis x and the straight lines 0Q' and 0Q be '_0' and ', respectively, and let the angle between the direction of the principal stress σ ₁ in the x-y plane and the x-axis be γ, and the direction of the above principal stress. The angle between and the straight line 0Q is the straight line 0'P
Let ω be the angle between and 0'P'. In addition, the strain in the crystal lattice plane normal to the straight line 0P is ε〓, the principal stress in the x-y plane is σ ₁ , σ ₂ , the stress in the direction of the straight line 0Q is σ, the Young's modulus is E, and the Poisson's ratio is ν. Then, as is well known, ε=1+ν/Eσsin ² ψ−ν/E(σ ₁ +σ ₂
)...(1) holds true. And, between the principal stress and the stress in any direction, there is a Mohr stress circle relationship σ=1/2 {(σ ₁ +σ ₂ )+(σ ₁ −σ ₂ )cos2} …(2), Substituting equation (2) into equation (1), ε=1+ν/2E{(σ ₁ +σ ₂ )+(σ ₁ −σ ₂ )cos2}sin ² ψ−ν/E(σ ₁ +σ ₂ )... (3) is obtained. Further, if the diffraction angle of the incident X-ray χ by the crystal lattice plane normal to the straight line 0P in Fig. 1 is 2θ, and the reference diffraction angle by the unstrained lattice plane is θ ₀ , then ε〓=−(θ−θ ₀ )・cotθ ₀ (4). From the above equations (3) and (4), is obtained.

As shown in FIG. 1, the direction γ of the principal stress is in a state where the angle in equation (5) is 0, and at this time the diffraction angle 2θ takes a minimum or maximum value. And since the angle is the angle ('-γ), by fixing the angles ψ ₀ and ω in Figure 1 and changing the angle ' while keeping the angle ψ in equation (5) constant, we can calculate the diffraction angle. By observing the position where 2θ is maximum or minimum, the direction γ of the principal stress can be determined. That is, while keeping the angle ω in FIG. 1 constant, the direction of the incident X-ray χ is changed so that the point 0' moves on a circle C having the normal z as its axis. Figure 2 is a graph that shows the relationship between the angle ' and the diffraction angle 2θ through such operations.By varying the angle ' within a range of approximately 90 degrees, the position γ where 2θ is maximum or minimum can be detected. can do.

Furthermore, if we draw a graph showing the relationship between the diffraction angle 2θ and cos2('-γ) using the direction γ of the principal stress determined as described above, we will obtain a straight line as shown in Figure 3. It will be done. As is clear from equation (5), the slope of this straight line is A, and the value of 2θ at the position where cos2 ('-γ) is 0 is B. Therefore, the reference diffraction angle θ ₀
If σ 1 and σ 2 are known, the magnitudes σ ₁ and σ ₂ of the principal stress can be determined by applying these values A and B to equation (5). If the reference diffraction angle θ ₀ is not known, the angle ψ ₀ in FIG. 1 and therefore the angle ψ are changed in two steps and two observations are made before and after, thereby drawing two straight lines in FIG. 3. It is possible to obtain the principal stresses σ ₁ and σ ₂ with extremely accurate approximation from the coordinate values of the intersection of these two straight lines or the coordinate values of the virtual intersection obtained by extending the above two straight lines, and the slope of the straight line. can. In this case, the observed values corresponding to the above two straight lines are expressed by the angle ' and the diffraction angle 2θ as shown in Figure 2.
If _two curves are obtained by blotting as the relationship between or is displayed.

As described above, the stress measurement method of the present invention maintains the angle ψ ₀ between the point 0 to be measured and the normal z constant, and makes X-rays χ incident on the point 0 from multiple directions. Diffraction angle 2 of X-rays containing each incident X-ray and diffracted in a direction forming an arbitrary constant angle P0P' with respect to the plane 0-0'-P'-Q' perpendicular to the sample surface.
The direction or magnitude of the principal stress is determined by observing θ in each of the plurality of incident directions. Therefore, the direction of the principal stress can be detected very easily, and since the X-ray source is moved only continuously or intermittently along one circular arc, the operability of the apparatus is also good. and incident X
Keeping the angle between the line and the normal constant, the line source is approximately 90
Since the point to be measured is only moved within a range of degrees, there is an effect that measurement can be easily performed even when there is no wide space around the point to be measured.

[Brief explanation of the drawing]

FIG. 1 is a diagram for explaining the principle of the present invention,
FIGS. 2 and 3 are examples of graphs observed by the method of the present invention. In the figure, 0
is the measured point on the sample surface, z is the normal line to the sample surface, X is the incident X-ray, C is the locus of movement of point 0' on the incident X-ray, S is the X-ray diffraction surface normal ring, σ ₁ , σ ₂ is the principal stress.

Claims (1)

[Claims] 1. Inject X-rays of a single wavelength onto a point to be measured on a polycrystalline sample surface from multiple directions with equal angles to the normal line erected at that point, and The diffraction angles of X-rays diffracted in directions forming an arbitrary fixed angle with respect to a plane perpendicular to the plane are observed for each of the plurality of incident directions, and the direction of the principal stress and its direction are determined from each measurement value. X characterized by seeking at least one of the size and
Linear stress measurement method.